Just please note that the Lossy Inductance adjustment is not intended to be a perfectly accurate representation - it's just the best tool for the job that we've come up with when using a generic formula to alter a single parameter to make sims match measurements. Having said that it's a lot better than ignoring the issue, just want to make sure it's clear that it's not a perfect solution and won't always give perfectly accurate results. As you can see by looking at the scatter chart in the paper, some of the drivers follow the trend line pretty closely while others are clearly outliers. The trend line is the adjustment formula and not all drivers fit the trend line all as well as others.
Apart from the generic formula that Hornresp calculates there is a more accurate way to derate Bl but it requires making your own sealed box and measuring the driver and comparing the measurement to a sim and then adjusting Bl to make the sim match the measurement. This is the first step in the generic formula creation, it's how the generic formula was derived. This will be the most accurate value to use for Bl, matching a sim to a measurement. But it does require quite a bit more input - you need the driver in hand, you need to build a sealed box and you need to measure and sim it. But this way you get the best derated Bl value possible and you know it isn't an outlier in the generic formula.
Anyway, very pleased you give the Lossy Inductance tool attention, just want to make sure you understand how and why it's not perfect. Still a lot better than not using it but not perfect.
Hi 'just a guy',
Can you share the generic formula and how it is implied in Hornresp?
Regards,
Djim
This is the lossy inductance Bl adjustment formula -
Adjusted Bl = (0.7234 - 0.0782 x Ln (Le/Re)) x Original Bl
It's in the paper I wrote, I think I already linked to the paper earlier in this thread but here it is again. Large Coil Simulation Accuracy Issue And Adjustment - amateur audio
Hornresp simply runs that formula and internally adjusts the value of Bl if you use the lossy inductance tool either from the main screen or in the loudspeaker wizard.
Adjusted Bl = (0.7234 - 0.0782 x Ln (Le/Re)) x Original Bl
It's in the paper I wrote, I think I already linked to the paper earlier in this thread but here it is again. Large Coil Simulation Accuracy Issue And Adjustment - amateur audio
Hornresp simply runs that formula and internally adjusts the value of Bl if you use the lossy inductance tool either from the main screen or in the loudspeaker wizard.
I'm not good at math and I don't know the answers to those questions. I made a scatter chart in Excel with all the drivers based on Le/Re vs curve fit Bl, then I had Excel make a log trendline to describe the data trend, then Excel generated the formula that I showed. Ln is some form of higher math term that I don't understand. A quick search shows it might mean "natural logarithm".
I don't really understand any of the math but David McBean helped with that part. All I did was plot my data on a scatter chart and Excel and David took over from there to interpret the data into a useful formula.
None of this will be very clear though unless you read the paper. It's all quite neatly summarized in the paper with pictures so you can follow along and see exactly how the formula was constructed, what data it incorporates and how it is used.
I don't really understand any of the math but David McBean helped with that part. All I did was plot my data on a scatter chart and Excel and David took over from there to interpret the data into a useful formula.
None of this will be very clear though unless you read the paper. It's all quite neatly summarized in the paper with pictures so you can follow along and see exactly how the formula was constructed, what data it incorporates and how it is used.
Are you talking about my generic adjustment vs simply replacing replacing Re with Zmin providing equally accurate results?
In that case, I'd encourage you to try to find a value for Zmin for any of the 22 drivers in the study. Not even the Dayton spec sheets list Zmin, so good luck finding it from other smaller manufacturers in the list like Fi, Stereo Integrity, Sundown, RE, etc.
So if you are able to find a value for Zmin for any of the 22 drivers in the study, I'd encourage you to use that value for Zmin instead of Re in a sim and post the results and see if your results are more accurate than my generic formula provides.
I can guarantee you that my generic adjustment will be more accurate.
The only polite way to say this is, "it is a fudge factor"*. It's just an interpreted figure that makes some of the data for some of the drivers some of the time sort of look sort of better.
Leach and others long ago demonstrated that voicecoil inductance seems not to quite fit the ancient model of a pure inductance and seemed to be "lossy". An interesting finding but nobody seemed especially bothered since it wasn't clear what was going on and didn't matter much in making speakers.
Entirely unlike the ancient electrical equivalents model from which Thiele devised a good practical system of calculation for driver enclosures, this fudge factor has no conceptual foundation what so ever. Just all fudge: a numeric dodge.
Being without conceptual basis, hard to know when it is smart to use it and when not. Take your pick.
As an empirically cobled together fudge factor (even without conceptual basis), it can be make loose estimates less loose... sometimes. But it certainly doesn't advance anybody's understanding of what is going on with drivers and enclosures.
B.
* As Wikipedia says, "A fudge factor is an ad hoc quantity or element introduced into a calculation, formula or model in order to make it fit observations or expectations"
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Absolutely it's a fudge factor, but when I can consistently show that it improves the accuracy of a model 100 percent of the time, what else can you ask for?
I'm not at Leach's level, I'm not good at math. I've simply provided a way to make sims more accurate in every case, at least when using these drivers with high normalized Le.
If you check the paper I wrote you will find that there's a surprising amount of conceptual foundation, a lot of which was based on intuition which in turn is based on years of experience, I know you think I just randomly changed something and found some small improvement in a few random cases but that's not at all how this adjustment was developed. If it was I never would have found peer interest, support and criticism at the high levels of esteem that these gentlemen brought to the table.
As far as furthering understanding of drivers and enclosures - the paper and the adjustment make it very clear that the issue is lossy inductance, the issue presents as a decrease in apparent motor strength compared to what the simple t/s indicate, and the adjustment when used in a sim create a more accurate picture of your measured response. 100 percent of the time, What remains unclear about any of this? True, the issue itself has not been mathematically modeled by me, but Leach and Wright already did that so go read their papers if you want further understanding. I'm simply providing a more accurate model without needing complex inductance specs so you can perform a simple adjustment for any given driver that has listed t/s specs.
The wiki definition is exactly right in describing this adjustment - it's a specific adjustment based on empirical evidence added to a model to make it fit measured observations, and furthermore it works 100 percent of the time. It's not completely accurate, but it can't be, considering drivers are constructed differently and will measure differently, the adjustment itself is generic and based on a sampling of different drivers, and only one parameter is adjusted. Based on that it's a wonder that the adjustment works at all, but I'm shown empirically that it works quite well in 100 percent of the cases when using these high normalized Le drivers.
I'm not at Leach's level, I'm not good at math. I've simply provided a way to make sims more accurate in every case, at least when using these drivers with high normalized Le.
If you check the paper I wrote you will find that there's a surprising amount of conceptual foundation, a lot of which was based on intuition which in turn is based on years of experience, I know you think I just randomly changed something and found some small improvement in a few random cases but that's not at all how this adjustment was developed. If it was I never would have found peer interest, support and criticism at the high levels of esteem that these gentlemen brought to the table.
As far as furthering understanding of drivers and enclosures - the paper and the adjustment make it very clear that the issue is lossy inductance, the issue presents as a decrease in apparent motor strength compared to what the simple t/s indicate, and the adjustment when used in a sim create a more accurate picture of your measured response. 100 percent of the time, What remains unclear about any of this? True, the issue itself has not been mathematically modeled by me, but Leach and Wright already did that so go read their papers if you want further understanding. I'm simply providing a more accurate model without needing complex inductance specs so you can perform a simple adjustment for any given driver that has listed t/s specs.
The wiki definition is exactly right in describing this adjustment - it's a specific adjustment based on empirical evidence added to a model to make it fit measured observations, and furthermore it works 100 percent of the time. It's not completely accurate, but it can't be, considering drivers are constructed differently and will measure differently, the adjustment itself is generic and based on a sampling of different drivers, and only one parameter is adjusted. Based on that it's a wonder that the adjustment works at all, but I'm shown empirically that it works quite well in 100 percent of the cases when using these high normalized Le drivers.
If Ben or Djim would like to consider speaking more about the lossy inductance adjustment method specifically then maybe consider starting a new thread. There were a few things MMJ needed to know about the adjustment and he knows what he needs to know now. Discussing this adjustment specifically in a way that doesn't relate to his thread topic is wrecking his thread so start a new one if you want to continue this.
Thanks for the sentiment but this math seems wrong. Try letting Hornresp calculate - I'm not sure if it's a math error or using Djim's shortcut which doesn't follow BEDMAS.
At the outside the worst of the problem drivers were showing about 30 percent apparent motor strength decrease IIRC, MMJ found one with a bit worse performance than that a few posts ago IIRC, but my study never found losses in the range of 56 percent or higher I don't think. I'd have to reread the paper to verify but that sound really high and out of the range of what I remember.
Letting Hornresp run the adjustment formula instead of following Djim's shortcut (which incidentally does not follow basic 6th grade math rules of which order to do calculations) we get this for the two quoted examples.
Original BL = 40, Le = 2.5mH, Re = 5.2, NEW BL = 31.23 = ~22% Decrease !
Original BL = 40, Le = 3.5mH, Re = 5.2, NEW BL = 30.17 = ~25% Decrease !
So for whatever reason your calculations were off by a bit which is relatively pronounced since your lower normalized Le example gave a higher loss estimate than the higher normalized Le example.
But still, losses in the range of 25 percent apparent motor strength are no joke - you can't take away 1/4 of your motor generated force and expect your sims to be accurate.
So even though your calculations were off by a bit this is still very important stuff so thanks for bringing it up.
I'm not all that good at long maths eitherBut this isn't
Original BL = 40, Le = 2.5mH, Re = 5.2, NEW BL = 12.4 = 69% Decrease !
Original BL = 40, Le = 3.5mH, Re = 5.2, NEW BL = 17.37 = 56.5% Decrease !
Hi Zero D,
It would appear that you used the following formula:
Adjusted Bl = 0.6452 * Le / Re * Original Bl
With the value of Le expressed in millihenrys.
The formula you should have used is:
Adjusted Bl = (0.7234 - 0.0782 * Ln(Le / Re)) * Original Bl
Where Ln(Le / Re) is the natural logarithm of Le / Re, and the value of Le is expressed in henrys, not millihenrys.
(Note that the Djim "simplification" is not correct).
Kind regards,
David
I fully appreciate this improved version of impeferfection ;-)
Just A Guy,
I understand that it is not an entirely perfect solution but if it does indeed get us closer to what we will end up with in the real-world then i am very happy with that
.... I see that as progress..
Since it would be dauntingly inconvenient for me to obtain all of these different drivers which we discuss here and put them into sealed boxes in order to measure discrepancies etc etc etc I see this "Lossy Le" feature as the next best thing .....It is practical and it's level of accuracy will be close enough for what i do ..... Works for me
Just A Guy,
I understand that it is not an entirely perfect solution but if it does indeed get us closer to what we will end up with in the real-world then i am very happy with that
.... I see that as progress..Since it would be dauntingly inconvenient for me to obtain all of these different drivers which we discuss here and put them into sealed boxes in order to measure discrepancies etc etc etc I see this "Lossy Le" feature as the next best thing .....It is practical and it's level of accuracy will be close enough for what i do ..... Works for me
It would perhaps be more appropriate to be quoting from the Wikipedia entry for curve fitting. There is nothing arbitrary about the formula used in Hornresp.
CORRECTION:
Where Ln(Le / Re) is the natural logarithm of Le / Re, and the value of Le is expressed in millihenrys.
(Hornresp normally requires values of Le to be expressed in henrys, but not in this case).
I took "fudge factor" to simply mean my model (including the entire dissection of the cause) was not as mathematically fastidiously explained as well as Leach's approach to lossy inductance and also not perfectly accurate, and on that I'm willing to agree.
But you are certainly correct, there's nothing at all arbitrary about the formula or how it was created, everything from start to finish in the adjustment formula was done for very good reason and documented in the paper, which apparently some people can't be bothered to read or we wouldn't have discussions like this popping up every so often from the same usual suspects.
15s definitely work
USRFobiwan,
Dual 15s can be a great way to go .... The 15SW115 looks like a solid option and two of them have plenty of displacement, considerably more cone area than an 18" driver, and the combined motor force is substantial , so i would fully expect two of those 15s to easily surpass the performance of a single 18SW115 .....
For ultimate portability I can get the cabinet size down for a single 15 .... Would be easy enough for a single person to maneuver around and would work very well in arrays.... Considering that the price of the 15SW115 is similar to it's 18" sibling this may not be the most budget conscious (decibel per dollar) option but i have no doubt that it would be a spectacular performer .....
For a low-budget PA option the 15LB100 sold by Thomann would work .... It just has less power handling and less linear excursion than the B&C .. (we do have verified measured parameters for this particular driver)...
I modeled a pair of the Twisted 15s the other day in a 32hz tuned Super Planar 8th and was surprised to see such fantastic performance while only requiring 600 liters net for the pair at this tuning .... Of course this was using their published parameters .... Still waiting for someone to measure one of these to verify the parameters ... ........
The Skar DDX 15 drivers also have a lot of potential if their parameters match what Skar publishes, although the cabinet volume required for two would be a little more for the set even with a 35hz tuning (if a Super Planar 8th) .....NOTE: Ideally it would be best to have measured parameters to be sure...
There are a lot of these DDX sub drivers being used out there currently, so someday we will hopefully get one or a few measured with the right equipment (DATS , or S&L Woofer Tester , or an REW rig or whatever) ............................. A friend of ours has been considering a dealer's agreement with Skar lately, so if he goes through with that then he will get the opportunity to handle and measure many of them at his shop .. .
USRFobiwan,
Dual 15s can be a great way to go .... The 15SW115 looks like a solid option and two of them have plenty of displacement, considerably more cone area than an 18" driver, and the combined motor force is substantial , so i would fully expect two of those 15s to easily surpass the performance of a single 18SW115 .....
For ultimate portability I can get the cabinet size down for a single 15 .... Would be easy enough for a single person to maneuver around and would work very well in arrays
.... Considering that the price of the 15SW115 is similar to it's 18" sibling this may not be the most budget conscious (decibel per dollar) option but i have no doubt that it would be a spectacular performer ..... For a low-budget PA option the 15LB100 sold by Thomann would work .... It just has less power handling and less linear excursion than the B&C .. (we do have verified measured parameters for this particular driver
)...I modeled a pair of the Twisted 15s the other day in a 32hz tuned Super Planar 8th and was surprised to see such fantastic performance while only requiring 600 liters net for the pair at this tuning .... Of course this was using their published parameters .... Still waiting for someone to measure one of these to verify the parameters ... ........
The Skar DDX 15 drivers also have a lot of potential if their parameters match what Skar publishes, although the cabinet volume required for two would be a little more for the set even with a 35hz tuning (if a Super Planar 8th) .....NOTE: Ideally it would be best to have measured parameters to be sure...
There are a lot of these DDX sub drivers being used out there currently, so someday we will hopefully get one or a few measured with the right equipment (DATS , or S&L Woofer Tester , or an REW rig or whatever) ............................. A friend of ours has been considering a dealer's agreement with Skar lately, so if he goes through with that then he will get the opportunity to handle and measure many of them at his shop .. .
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